A device for driving at least one wheel of an aircraft landing gear including at least one landing gear wheel, this wheel including a rim, an electric motor including a shaft, a mechanical transmission system between the shaft of the motor and the rim, this mechanical transmission system including a mechanical reducer including a sun gear secured in rotation to the shaft of the motor, a ring gear, and planet gears which are carried by a planet carrier and which each includes three external toothings, including a median external toothing which is meshed with a toothing of the sun gear, and two lateral external toothings which are respectively meshed with toothings of the ring gear.